lahef

clahef

Functions

void clahef(
    const char*          uplo,
    const INT            n,
    const INT            nb,
          INT*           kb,
          c64*  restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          c64*  restrict W,
    const INT            ldw,
          INT*           info
);

void clahef(const char *uplo, const INT n, const INT nb, INT *kb, c64 *restrict A, const INT lda, INT *restrict ipiv, c64 *restrict W, const INT ldw, INT *info)

CLAHEF computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.

The partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**H U22**H )

A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0      I     )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U.

CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ‘U’) or A22 (if UPLO = ‘L’).

Parameters

in

uplo

• 'U': Upper triangular

• 'L': Lower triangular

in

n

The order of the matrix A. n>=0.

in

nb

The maximum number of columns of the matrix A that should be factored. nb should be at least 2 to allow for 2-by-2 pivot blocks.

out

kb

The number of columns of A that were actually factored. kb is either nb-1 or nb, or n if n<=nb.

inout

A

Single complex array of dimension (lda,n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part contains the upper triangular part. If uplo='L', the leading n-by-n lower triangular part contains the lower triangular part. On exit, A contains details of the partial factorization.

in

lda

The leading dimension of A. lda>=max(1,n).

out

ipiv

Integer array of dimension n. Details of the interchanges and the block structure of D. If uplo='U': only the last kb elements of ipiv are set. If ipiv[k] >= 0, rows and columns k and ipiv[k] were interchanged, D(k,k) is a 1-by-1 diagonal block. If ipiv[k] < 0, rows and columns k-1 and -(ipiv[k]+1) were interchanged, D(k-1:k,k-1:k) is a 2-by-2 block, and ipiv[k-1] = ipiv[k]. If uplo='L': only the first kb elements of ipiv are set. If ipiv[k] >= 0, rows and columns k and ipiv[k] were interchanged, D(k,k) is a 1-by-1 diagonal block. If ipiv[k] < 0, rows and columns k+1 and -(ipiv[k]+1) were interchanged, D(k:k+1,k:k+1) is a 2-by-2 block, and ipiv[k+1] = ipiv[k].

out

W

Single complex array of dimension (ldw,nb). Workspace for storing updated columns during factorization.

in

ldw

The leading dimension of W. ldw>=max(1,n).

out

info

• info=0: successful exit

• info>0: if info=k+1, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

zlahef

Functions

void zlahef(
    const char*          uplo,
    const INT            n,
    const INT            nb,
          INT*           kb,
          c128* restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          c128* restrict W,
    const INT            ldw,
          INT*           info
);

void zlahef(const char *uplo, const INT n, const INT nb, INT *kb, c128 *restrict A, const INT lda, INT *restrict ipiv, c128 *restrict W, const INT ldw, INT *info)

ZLAHEF computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.

The partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
      ( 0  U22 ) (  0   D  ) ( U12**H U22**H )

A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
      ( L21  I ) (  0  A22 ) (  0      I     )

where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U.

ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ‘U’) or A22 (if UPLO = ‘L’).

Parameters

in

uplo

• 'U': Upper triangular

• 'L': Lower triangular

in

n

The order of the matrix A. n>=0.

in

nb

The maximum number of columns of the matrix A that should be factored. nb should be at least 2 to allow for 2-by-2 pivot blocks.

out

kb

The number of columns of A that were actually factored. kb is either nb-1 or nb, or n if n<=nb.

inout

A

Double complex array of dimension (lda,n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part contains the upper triangular part. If uplo='L', the leading n-by-n lower triangular part contains the lower triangular part. On exit, A contains details of the partial factorization.

in

lda

The leading dimension of A. lda>=max(1,n).

out

ipiv

Integer array of dimension n. Details of the interchanges and the block structure of D. If uplo='U': only the last kb elements of ipiv are set. If ipiv[k] >= 0, rows and columns k and ipiv[k] were interchanged, D(k,k) is a 1-by-1 diagonal block. If ipiv[k] < 0, rows and columns k-1 and -(ipiv[k]+1) were interchanged, D(k-1:k,k-1:k) is a 2-by-2 block, and ipiv[k-1] = ipiv[k]. If uplo='L': only the first kb elements of ipiv are set. If ipiv[k] >= 0, rows and columns k and ipiv[k] were interchanged, D(k,k) is a 1-by-1 diagonal block. If ipiv[k] < 0, rows and columns k+1 and -(ipiv[k]+1) were interchanged, D(k:k+1,k:k+1) is a 2-by-2 block, and ipiv[k+1] = ipiv[k].

out

W

Double complex array of dimension (ldw,nb). Workspace for storing updated columns during factorization.

in

ldw

The leading dimension of W. ldw>=max(1,n).

out

info

• info=0: successful exit

• info>0: if info=k+1, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.